Whether it is kind or unkind, it's an important distinction.
Not all the CEV are in the third primary/booster as fourth shot group. Indeed 4/5 of them aren't.
Those who are, by and large, know about it - the roll out was a shambles, but finally consultants and GPs did get invitations issued. (See several MN threads passim where those of us who were struggling to get jabs for ourselves or household members shared the frustrations - or rather don't, unless you're feeling masochistic thus morning)
If you've just realised to might be eligible but have been missed, the best thing to do is get on to consultant's team and or GP who should be able to change your vaccination record, and then you should be called for fourth 3 months after your third primary (if original plan had worked, these wouid be starting now, given fuck ups they won't be falling due until mid Jan and onwards)
But when someone just says 'CEV' then 80% of the time the reason they haven't been notified is because they aren't entitled. Only the severely immune suppressed are (sometimes now called the critically vulnerable - but that doesnt seem to have made it to a new and useful acronym)